An unmyelinated section of membrane in a nerve axon has a resting potential diff

Question

An unmyelinated section of membrane in a nerve axon has a resting potential difference, V = -70mV. Taking the membrane thickness to be 3 nm and the capacitance per unit area of membrane to be 2.0 x 10-2 F m-2. a) Determine how much excess charge per m^2 is located on either side of the membrane. b) Determine the dielectric constant for the membrane c) Determine the capacitive energy stored in the membrane for a 1 mm long section of the axon where the radius is 3 microns, and comment on an advantage of axon myelination in relation to this.

Explanation / Answer

charge , Q = C*V = 2*10^-2*70*10^-3 = 0.0014 C

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cpacitance C = k*eo*A/d

capacitance / m^2 = K*eo/d

2*10^-2 = k*8.85*10^-12/(3*10^-9)

Di electric constant k = 6.78 <<<--------answer

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energy stored E = (1/2)*C*v^2*A = (1/2)*2*10^-2*(70*10^-3)^2*pi*(3*10^-6)^2 = 1.385*10^-15 J

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